<p>siserune, in response to your question whether the multiplicative approach is the only viable one for an individual applicant who is working with pH, pY and pP (as opposed to rH, rY, and rP): yes. I think so. </p>
<p>Still, there are assumptions that go into this. I am assuming that there is a probabilistic aspect to the decision-making, even after all of the differences in the strength of the applications have been taken into account. I base this assumption on my experience on selection committees, though not in an Ivy-admissions context. But it’s possible that the whole process is entirely deterministic. I am also assuming that each college makes its decisions without knowledge of any other college’s decisions. I’m quite a bit more confident of this. There may be other assumptions that I haven’t noticed yet.</p>
<p>I’m usually comfortable calling a string of equations “nonsense,” if they are. I’m a lot less comfortable calling an English-language discussion of a mathematical idea “nonsense,” because issues can arise in the math-to-English conversion, and there might be an interesting idea behind the words.</p>